Highlighted in green.
I am not sure what $\ A_1\setminus A_0$ equals to... if $A_0=\emptyset$.
I suspect that $\ A_1\setminus A_0$ equals $A_1$. The fact that $A_0=\emptyset$ makes me reason that $\ A_1\setminus\emptyset$ implies $\ A_1\setminus A_0=A_1$ because $\ A_1\setminus\emptyset$ equals "$\ A_1$ without the $\emptyset$". Which is impossible because $\ A_1\setminus\emptyset$ with always consist of $\emptyset$ (general property of empty sets) hence $\ A_1\setminus A_0=A_1$.
Is my reasoning correct? (in addition forgive me in advance for misconceptions of treating the empty set as an element or subset.......)
Post is linked to: Events $A_n\uparrow A$ meaning. $A_n\downarrow A$ meaning.